CARD #12 • GOLD 300 PTS
Simplify the Expression
\( -\frac{4}{7}r + \frac{3}{2}s - \frac{5}{14}r - \frac{5}{4}s + 4 - \frac{9}{2} \)
LCD: 14 for \(r\), 4 for \(s\), 2 for constants Fractions (Mixed LCD)
CARD #13 • TITAN BOSS 500 PTS
Simplify the Expression
\( \frac{3}{4}x - 2.5y + 11 - 1.25x + \frac{7}{2}y - 18 \)
Convert \(\frac{3}{4} \leftrightarrow 0.75\) or decimals to fractions Hybrid (Dec + Frac)
CARD #14 • TITAN BOSS 500 PTS
Simplify the Expression
\( -4.2a + \frac{2}{5}b - 3.8 - \frac{4}{5}a - 1.6b + 9 \)
Notice \(\frac{2}{5}=0.4\) and \(\frac{4}{5}=0.8\) Hybrid (Dec + Frac)
CARD #15 • TITAN BOSS 500 PTS
Simplify the Expression
\( -\frac{5}{6}w + 3.75z - \frac{1}{3}w - 1.25z - 8.4 + 2.9 \)
Fraction \(w\)-terms • Decimal \(z\)-terms Hybrid Complex
CARD #16 • TITAN BOSS 500 PTS
Simplify the Expression
\( 2.8m - \frac{3}{4}n + 4.5p - 5.3m + \frac{7}{8}n - 1.5p - 6 \)
3 variables (\(m, n, p\)) + constant! Ultimate Titan
Term Titans • Page 2 of 2 Final expressions should be in alphabetical variable order!
Tier Points: [ 500 ] Score Earned: [ ] pts
1. Group Like Terms & Convert Formats
2. Combined Calculations
3. Simplified Form
Captain Sign: _____
Page 1 Subtotal: ________ pts
Page 2 Subtotal: ________ pts
Clean Grouping Bonus: + _______ pts
GRAND TOTAL: ________ pts
Which coefficient type was most challenging today (integers, decimals, or fractions)? What strategy helped your team conquer it?
Term Titans • Page 2 of 2 Great mathematicians always double-check their negative signs!
Championship Rounds
Rounds 3 & 4: Fractions & Titan Hybrids
CARD #09 • 300 PTS Tier: Gold
\( \frac{2}{3}x - \frac{1}{4}y + 5 - \frac{1}{6}x + \frac{3}{4}y - 8 \)
LCD: \(x\): \(\frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2}\); \(y\): \(-\frac{1}{4} + \frac{3}{4} = \frac{2}{4} = \frac{1}{2}\)
\( \frac{1}{2}x + \frac{1}{2}y - 3 \) Std. Form
• Constants: \(5 - 8 = -3\).
CARD #10 • 300 PTS Tier: Gold
\( -\frac{3}{5}a + \frac{7}{10}b - 2 - \frac{1}{2}a - \frac{2}{5}b + \frac{3}{4} \)
LCD: \(a\): \(-\frac{6}{10} - \frac{5}{10} = -\frac{11}{10}\); \(b\): \(\frac{7}{10} - \frac{4}{10} = \frac{3}{10}\)
\( -\frac{11}{10}a + \frac{3}{10}b - \frac{5}{4} \) Std. Form
• Const: \(-2 + \frac{3}{4} = -\frac{8}{4} + \frac{3}{4} = -\frac{5}{4}\).
CARD #11 • 300 PTS Tier: Gold
\( \frac{5}{8}c - \frac{2}{3}d - \frac{7}{8}c + \frac{1}{6}d + \frac{1}{2} - \frac{5}{6} \)
LCD: \(c\): \(-\frac{2}{8} = -\frac{1}{4}\); \(d\): \(-\frac{4}{6} + \frac{1}{6} = -\frac{3}{6} = -\frac{1}{2}\)
\( -\frac{1}{4}c - \frac{1}{2}d - \frac{1}{3} \) Std. Form
• Const: \(\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}\).
CARD #12 • 300 PTS Tier: Gold
\( -\frac{4}{7}r + \frac{3}{2}s - \frac{5}{14}r - \frac{5}{4}s + 4 - \frac{9}{2} \)
LCD: \(r\): \(-\frac{8}{14} - \frac{5}{14} = -\frac{13}{14}\); \(s\): \(\frac{6}{4} - \frac{5}{4} = \frac{1}{4}\)
\( -\frac{13}{14}r + \frac{1}{4}s - \frac{1}{2} \) Std. Form
• Const: \(\frac{8}{2} - \frac{9}{2} = -\frac{1}{2}\).
CARD #13 • 500 PTS Tier: Titan
\( \frac{3}{4}x - 2.5y + 11 - 1.25x + \frac{7}{2}y - 18 \)
Work: \(0.75x - 1.25x = -0.5x\); \(-2.5y + 3.5y = 1y\)
\( -0.5x + y - 7 \) or \( -\frac{1}{2}x + y - 7 \) Both OK
• Emphasize: \(1y\) is written simply as \(y\).
CARD #14 • 500 PTS Tier: Titan
\( -4.2a + \frac{2}{5}b - 3.8 - \frac{4}{5}a - 1.6b + 9 \)
Work: \(-4.2a - 0.8a = -5a\); \(0.4b - 1.6b = -1.2b\)
\( -5a - 1.2b + 5.2 \) or \( -5a - \frac{6}{5}b + \frac{26}{5} \) Both OK
• Const: \(-3.8 + 9 = +5.2\).
CARD #15 • 500 PTS Tier: Titan
\( -\frac{5}{6}w + 3.75z - \frac{1}{3}w - 1.25z - 8.4 + 2.9 \)
Work: \(-\frac{5}{6}w - \frac{2}{6}w = -\frac{7}{6}w\); \(3.75z - 1.25z = 2.5z\)
\( -\frac{7}{6}w + 2.5z - 5.5 \) or \( -\frac{7}{6}w + \frac{5}{2}z - \frac{11}{2} \) Both OK
• Const: \(-8.4 + 2.9 = -5.5\).
CARD #16 • 500 PTS Tier: Titan
\( 2.8m - \frac{3}{4}n + 4.5p - 5.3m + \frac{7}{8}n - 1.5p - 6 \)
Work: \(2.8 - 5.3 = -2.5m\); \(-\frac{6}{8} + \frac{7}{8} = \frac{1}{8}n\); \(4.5 - 1.5 = 3p\)
\( -2.5m + \frac{1}{8}n + 3p - 6 \) Std. Form
• 3 variables: check alphabetical ordering \(m, n, p\).
Term Titans Answer Key • Page 2 of 2 Equivalent decimal and fraction representations are both mathematically valid.
\( -1.25u + 6.8v - 0.75u - 9.4v + 8.1 - 12.6 \)
Whole Number Alert: \( -1.25u - 0.75u \) simplifies to a clean integer! End of Deck A • Ready for Fractions?
CARD #09 • DECK B Tier: Gold League
300 POINTS
Simplify the Expression
\( \frac{2}{3}x - \frac{1}{4}y + 5 - \frac{1}{6}x + \frac{3}{4}y - 8 \)
Common Denominators: Find the LCD for \(x\)-terms (\(3\) and \(6\)). Fractions (Basic LCD)
CARD #10 • DECK B Tier: Gold League
300 POINTS
Simplify the Expression
\( -\frac{3}{5}a + \frac{7}{10}b - 2 - \frac{1}{2}a - \frac{2}{5}b + \frac{3}{4} \)
Calculation Ace: Convert integer \( -2 \) to \( -\frac{8}{4} \) to combine with \( +\frac{3}{4} \). Fractions (LCD 10 & 4)
CARD #11 • DECK B Tier: Gold League
300 POINTS
Simplify the Expression
\( \frac{5}{8}c - \frac{2}{3}d - \frac{7}{8}c + \frac{1}{6}d + \frac{1}{2} - \frac{5}{6} \)
Reduce All Terms: Ensure every resulting fraction is simplified to lowest terms! Fractions (Simplifying)
CARD #12 • DECK B Tier: Gold League
300 POINTS
Simplify the Expression
\( -\frac{4}{7}r + \frac{3}{2}s - \frac{5}{14}r - \frac{5}{4}s + 4 - \frac{9}{2} \)
LCD Matchup: \(r\)-terms use LCD 14; \(s\)-terms use LCD 4; constants use LCD 2. Boss Battles Coming Next!
CARD #13 • TITAN BOSS Tier: Hybrid Arena
500 POINTS
Titan Boss Challenge: Hybrid Expression
\( \frac{3}{4}x - 2.5y + 11 - 1.25x + \frac{7}{2}y - 18 \)
Conversion Strategy: Convert \( \frac{3}{4} = 0.75 \) and \( \frac{7}{2} = 3.5 \) (or all to fractions)! Hybrid Formats
CARD #14 • TITAN BOSS Tier: Hybrid Arena
500 POINTS
Titan Boss Challenge: Hybrid Expression
\( -4.2a + \frac{2}{5}b - 3.8 - \frac{4}{5}a - 1.6b + 9 \)
Pro Tip: Fifth fractions convert smoothly into decimals (\( \frac{2}{5}=0.4 \), \( \frac{4}{5}=0.8 \)). Hybrid Formats
CARD #15 • TITAN BOSS Tier: Hybrid Arena
500 POINTS
Titan Boss Challenge: Hybrid Expression
\( -\frac{5}{6}w + 3.75z - \frac{1}{3}w - 1.25z - 8.4 + 2.9 \)
Strategy Split: Solve \(w\) in fractions and \(z\) in decimals for optimal speed! Hybrid Formats
CARD #16 • ULTIMATE FINALE Tier: 3 Variables + Constant
500 POINTS
The Grand Finale: Master Challenge
\( 2.8m - \frac{3}{4}n + 4.5p - 5.3m + \frac{7}{8}n - 1.5p - 6 \)
All Roles Active: Combine \(m\)-terms, \(n\)-terms, \(p\)-terms, and preserve \( -6 \)! Tournament Final Round!
TT
Post-Game Debrief
Final Tally
1. Calculate Totals
Add Page 1 and Page 2 subtotal points on your recording sheet.
2. Grouping Bonus
+50 bonus points per card where like terms were boxed and rewritten!
3. Strategy Reflection
Discuss which coefficient type challenged your team the most.
Great work, Term Titans! Turn in your team recording sheets. Algebra Mastery Unlocked
